A consumer has preferences represented by the following utility function:

u (c1; c2) = ln c1 + ln c2,(0; 1)

where c1 is period 1 consumption, c2 is period 2 consumption and (0; 1)

represents a discount rate related to this consumer's preferences for time.1 The

consumer has 1 unit of time in each period. During the first period, he

can allocate his time between working units at a wage rate and study h units.

In the second period, the agent sells all his time on the labor market at a rate of

salary (1+2h), where h represents the time spent studying during the first period.

The salary of the second period, therefore, depends positively on the experience acquired during

the first period, , and investment in education, h. We assume that as well

experience that education positively affects second-period pay. This

implies that1 > 0 and2 > 0.

a) Write down this consumer's problem.

b) How much time will h*spend studying in the first period?

c) How does the wage rate, , influence the allocation between work and study

in the first period?

d) How does the discount rate,, influence the allocation between work and study

in the first period?

e) How does the return on experience,1, influence the allocation between work

and study in the first period?

f) How does the return on education,2, influence the allocation between work

and study in the first period?

g) Are there values of1,2 and such that this consumer will decide to allocate all

its time from the first period to study?

h) Are there values of1,2 and such that this consumer will decide to allocate all its time from the first period to work?